Long cycles in locally expanding graphs, with applications

TL;DR

This paper establishes conditions for long cycles in locally expanding graphs and applies these findings to areas like Ramsey theory, random graphs, and positional games.

Contribution

It introduces new conditions for long cycles in locally expanding graphs and demonstrates their applications across multiple combinatorial fields.

Findings

Conditions for long cycles in locally expanding graphs

Applications to Ramsey theory and random graphs

Techniques applicable to positional games

Abstract

We provide sufficient conditions for the existence of long cycles in locally expanding graphs, and present applications of our conditions and techniques to Ramsey theory, random graphs and positional games.